-7n(n-2)+2n(15+8)=6(-2n+9)

Solution for -7n(n-2)+2n(15+8)=6(-2n+9) equation:

Simplifying
-7n(n + -2) + 2n(15 + 8) = 6(-2n + 9)

Reorder the terms:
-7n(-2 + n) + 2n(15 + 8) = 6(-2n + 9)
(-2 * -7n + n * -7n) + 2n(15 + 8) = 6(-2n + 9)
(14n + -7n2) + 2n(15 + 8) = 6(-2n + 9)

Combine like terms: 15 + 8 = 23
14n + -7n2 + 2n(23) = 6(-2n + 9)

Reorder the terms for easier multiplication:
14n + -7n2 + 2 * 23n = 6(-2n + 9)

Multiply 2 * 23
14n + -7n2 + 46n = 6(-2n + 9)

Reorder the terms:
14n + 46n + -7n2 = 6(-2n + 9)

Combine like terms: 14n + 46n = 60n
60n + -7n2 = 6(-2n + 9)

Reorder the terms:
60n + -7n2 = 6(9 + -2n)
60n + -7n2 = (9 * 6 + -2n * 6)
60n + -7n2 = (54 + -12n)

Solving
60n + -7n2 = 54 + -12n

Solving for variable 'n'.

Reorder the terms:
-54 + 60n + 12n + -7n2 = 54 + -12n + -54 + 12n

Combine like terms: 60n + 12n = 72n
-54 + 72n + -7n2 = 54 + -12n + -54 + 12n

Reorder the terms:
-54 + 72n + -7n2 = 54 + -54 + -12n + 12n

Combine like terms: 54 + -54 = 0
-54 + 72n + -7n2 = 0 + -12n + 12n
-54 + 72n + -7n2 = -12n + 12n

Combine like terms: -12n + 12n = 0
-54 + 72n + -7n2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
7.714285714 + -10.28571429n + n2 = 0

Move the constant term to the right:

Add '-7.714285714' to each side of the equation.
7.714285714 + -10.28571429n + -7.714285714 + n2 = 0 + -7.714285714

Reorder the terms:
7.714285714 + -7.714285714 + -10.28571429n + n2 = 0 + -7.714285714

Combine like terms: 7.714285714 + -7.714285714 = 0.000000000
0.000000000 + -10.28571429n + n2 = 0 + -7.714285714
-10.28571429n + n2 = 0 + -7.714285714

Combine like terms: 0 + -7.714285714 = -7.714285714
-10.28571429n + n2 = -7.714285714

The n term is -10.28571429n.  Take half its coefficient (-5.142857145).
Square it (26.44897961) and add it to both sides.

Add '26.44897961' to each side of the equation.
-10.28571429n + 26.44897961 + n2 = -7.714285714 + 26.44897961

Reorder the terms:
26.44897961 + -10.28571429n + n2 = -7.714285714 + 26.44897961

Combine like terms: -7.714285714 + 26.44897961 = 18.734693896
26.44897961 + -10.28571429n + n2 = 18.734693896

Factor a perfect square on the left side:
(n + -5.142857145)(n + -5.142857145) = 18.734693896

Calculate the square root of the right side: 4.328359261

Break this problem into two subproblems by setting 
(n + -5.142857145) equal to 4.328359261 and -4.328359261.

Subproblem 1
n + -5.142857145 = 4.328359261

Simplifying
n + -5.142857145 = 4.328359261

Reorder the terms:
-5.142857145 + n = 4.328359261

Solving
-5.142857145 + n = 4.328359261

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '5.142857145' to each side of the equation.
-5.142857145 + 5.142857145 + n = 4.328359261 + 5.142857145

Combine like terms: -5.142857145 + 5.142857145 = 0.000000000
0.000000000 + n = 4.328359261 + 5.142857145
n = 4.328359261 + 5.142857145

Combine like terms: 4.328359261 + 5.142857145 = 9.471216406
n = 9.471216406

Simplifying
n = 9.471216406

Subproblem 2
n + -5.142857145 = -4.328359261

Simplifying
n + -5.142857145 = -4.328359261

Reorder the terms:
-5.142857145 + n = -4.328359261

Solving
-5.142857145 + n = -4.328359261

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '5.142857145' to each side of the equation.
-5.142857145 + 5.142857145 + n = -4.328359261 + 5.142857145

Combine like terms: -5.142857145 + 5.142857145 = 0.000000000
0.000000000 + n = -4.328359261 + 5.142857145
n = -4.328359261 + 5.142857145

Combine like terms: -4.328359261 + 5.142857145 = 0.814497884
n = 0.814497884

Simplifying
n = 0.814497884

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.471216406, 0.814497884}